Question

How do you identify all vertical asymptotes for `f(x)=1-3/(x-3)`?

Answer 1

vertical asymptote at x = 3

Explanation:

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non-zero for this value then it is a vertical asymptote.

solve: `x-3=0rArrx=3" is the asymptote"`

If you prefer you could consider f(x) as

`f(x)=(x-3)/(x-3)-3/(x-3)=(x-6)/(x-3)`

The end result is the same.
graph{(x-6)/(x-3) [-10, 10, -5, 5]}